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Classical Mechanics

Classical Mechanics

PHYS2501 4 hours

Classical Mechanics

The course covers vector algebra and vector differentiation, Newton’s Laws of motion and the rectilinear motion of a single particle. Also, the course covers the simple harmonic motion, the damped and forced harmonic oscillator. The course covers the general motion of a particle in three dimensions. Indeed, the study of non-inertial reference systems, as well as the central forces and celestial mechanics. The motion of a system of many particles is also covered in the course.
PHYS1101 General Physics 1
4 hours
1. Fundamental Concepts Vectors
? Revision of vectors
? Triple products
? Derivative of a vector.
? Position vector of a particle velocity and acceleration in rectangular coordinates.
? Velocity and acceleration in polar coordinates.
? Velocity and acceleration in cylindrical and spherical coordinates. 6
2. Newtonian Mechanics, Rectilinear Motion of a Particle
? Newton's law of motion.
? Rectilinear Motion: uniform Acceleration under a constant force.
? Position-dependent forces.
? The Concepts of kinetic and potential energy.
? Velocity-dependent forces.
? Fluid resistance and terminal velocity.
? Linear Resorting Force: harmonic motion.
? Energy considerations in harmonic motion.
? Damped harmonic motion.
? Forced harmonic motion: resonance. 10
3. General Motion of a Particle in Three Dimensions
? The potential energy function in three-dimensional motion
? The del operator
? Forces of the separable type.
? The harmonic oscillator in two and three dimensions.
? Constrained motion of a particle.
? Simple pendulum.
? More accurate solution of the simple pendulum problem. 12
4. Noninertial Reference Systems
• Accelerated coordinate systems and inertial forces.
• Rotating coordinate systems.
• Dynamics of a particle in a rotating coordinate system.
• Effects of earth's rotation.
• The Foucault pendulum. 10
5. Gravitation and Central Forces
• Introduction.
• Gravitational force between a uniform sphere and a particle.
• Kepler's laws of planetary motion.
• Kepler's second law: equal areas.
• Kepler's first law: The law of ellipses.
• Kepler's third law: The harmonic law.
• Potential energy in a gravitational field: gravitational potential.
• Potential energy in a general central field.
• Energy equation of an orbit in a central field.
• Orbital energies in an inverse-square field. 12
6. Dynamics of Systems of Particles
• Introduction.
• Center of mass and linear momentum of a system.
• Angular momentum and kinetic energy of a system.
• Motion of two interacting bodies: the reduced mass.
• Collisions.
• Oblique collisions and scattering: comparison of laboratory and
center of mass coordinates.
• Motion of a body with variable mass: rocket motion.